### Synopses & Reviews

Boundary element methods relate to a wide range of engineering applications, including fluid flow, fracture analysis, geomechanics, elasticity, and heat transfer. Thus, new results in the field hold great importance not only to researchers in mathematics, but to applied mathematicians, physicists, and engineers.

A two-day minisymposium Mathematical Aspects of Boundary Element Methods at the IABEM conference in May 1998 brought together top rate researchers from around the world, including Vladimir Maz ya, to whom the conference was dedicated. Focusing on the mathematical and numerical analysis of boundary integral operators, this volume presents 25 papers contributed to the symposium.

Mathematical Aspects of Boundary Element Methods provides up-to-date research results from the point of view of both mathematics and engineering. The authors detail new results, such as on nonsmooth boundaries, and new methods, including domain decomposition and parallelization, preconditioned iterative techniques, multipole expansions, higher order boundary elements, and approximate approximations. Together they illustrate the connections between the modeling of applied problems, the derivation and analysis of corresponding boundary integral equations, and their efficient numerical solutions.

#### Synopsis

A minisymposium at the IABEM conference in May 1998 brought together top rate researchers from around the world. Focusing on the mathematical and numerical analysis of boundary integral operators, this volume presents 25 papers contributed to the symposium. It provides up-to-date research results from the point of view of both mathematics and engineering. The authors detail new results and new methods. This volume illustrates the connections between the modeling of applied problems, the derivation and analysis of corresponding boundary integral equations, and their efficient numerical.

### Table of Contents

Coupling integral equations method and finite volume elements for the resolution of the Leontovich boundary value problem for the time-harmonic Maxwell equations in three dimensional heteregeneous media / H. Ammari and J.-C. Nedelec -- Smoothness properties of solutions to variational inequalities describing propagation of mode-1 cracks / M. Bach and S.A. Nazarov -- Edge singularities and Kutta condition for 3D unsteady flows in aerodynamics / P. Bassanini ... et al. -- Approximation using diagonal-plus-skeleton matrices / M. Bebendorf, S. Rjasanow and E.E. Tyrtyshnikov -- Variational integral formulation in the problem of elastic scattering by a buried obstacle / M. Ben Tahar, C. Granat and T. Ha-Duong -- Sensitivity analysis for elastic fields in non smooth domains / M. Bochniak and A.-M. Sèandig -- A formulation for crack shape sensitivity analysis based on Galerkin BIE, domain differentiation and adjoint variable / M. Bonnet -- Periodic and stochastic BEM for large structures embedded in an elastic half-space / D. Clouteau ... et al. -- Self-regularized hypersingular BEM for Laplace's equation / T.A. Cruse and J.D. Richardson -- An adaptive boundary element method for contact problems / C. Eck and W.L. Wendland -- Fast summation methods and integral equations / Y. Fu, J.R. Overfelt and G.J. Rodin -- Hybrid Galerkin boundary elements on degenerate meshes / I.C. Graham, W. Hackbusch and S.A. Sauter -- The Poincarâe-Steklov operator within countably normed spaces / N. Heuer and E.P. Stephan -- Boundary layer approximate approximations for the cubature of potentials / T. Ivanov, V. Maz'ya and G. Schmidt -- A simplified approach to the semi-discrete Galerkin method for the single-layer equation for a plate / D. Mauersberger and I.H. Sloan -- Construction of basis functions for high order approximate approximations / V. Maz'ya and G. Schmidt -- Lsubscript p-theory of direct boundary integral equations on a contour with peak / V. Maz'ya and A. Soloviev -- Essential norms of the integral operator corresponding to the Neumann problem for the Laplace equation / D. Medkovâa and J. Krâal -- Polynomial collocation methods for 1D integral equations with nonsmooth solutions / G. Monegato and L. Scuderi -- Singularities in discretized BIEs for Laplace's equation ; Trailing-edge conditions in aerodynamics / L. Morino and G. Bernardini -- Fluid-structure interaction problems / D. Natroshvili, A.-M. Sèandig and W.L. Wendland -- Extraction, higher order boundary element methods and adaptivity / H. Schulz, Ch. Schwab and W.L. Wendland -- Asymptotic solution of boundary integral equations / A. Sellier -- Sobolev multipliers in the theory of integral convolution operators / T. Shaposhnikova -- Stable boundary element approximations of Steklov-Poincarâe operators / O. Steinbach.